Blow-up for discrete Reaction-Diffusion Equations on Networks

Applicable Analysis and Discrete Mathematics

article

Soon-Yeong Chung¹  Jae-Hwang Lee² 

[1] Department of Mathematics and Program of Integrated Biotechnology, Sogang University;Department of Mathematics, Sogang University

关键词: Reaction-diffusion;    Discrete Laplacian;    Comparison principle;    Blow-up;   

DOI  :  10.2298/AADM150210005C

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

In this paper, we discuss the conditions under which blow-up occurs for thesolutions of reaction-diffusion equations on networks. The analysis of thisclass of problems includes the existence of blow-up in finite time and thedetermination of the blow-up time and the corresponding blow-up rate.In addition, when the solution blows up, we give estimates for the blow-uptime and also provide the blow-up rate. Finally, we show some numericalillustrations which describe the main results.

【 授权许可】

Unknown